The experiments presented here rely on Verificarlo [1]}, a tool that allows for the
perturbation and manipulation of floating-point data. Verificarlo is an LLVM-based compiler that instruments
floating-point instructions through different backends. The VPREC [2]} backend (for “Virtual
PRECision") was used here to simulate reduced floating-point formats. VPREC computes each instrumented ﬂoating-point
operation using the original format (double precision in our case) and rounds the result to the desired precision,
thereby ensuring correct rounding. VPREC also checks that the modified exponent is in the requested dynamic range \([e_{min}, e_{max}]\) , where \(e_{min}=2-2^{e-1}\)  and \(e_{max}=2^{e-1}-1\) .
